Area Situations

10 min

Narrative

This Number Talk encourages students to think about the relationship between division and fractions and the order of operations in order to strategically multiply whole numbers by fractions. The strategies elicited here will be helpful later in the lesson when students find the missing value in multiplication equations for a whole number and a fraction.
To use the properties of operations, students need to look for and make use of structure (MP7). In explaining strategies, students need to be precise in their word choice and use of language (MP6).

Launch

  • Display one problem.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategy.
  • Keep problems and work displayed.
  • Repeat with each problem.

Student Task

Find the value of each expression mentally.

  • 3×(10÷2)3 \times (10 \div 2)
  • 32×10\frac{3}{2} \times 10
  • (147)×10\left(\frac{14}{7}\right) \times 10
  • 14×10714 \times\frac{10}{7}

Sample Response

  • 15: I know 10÷2=510 \div 2 = 5 and 3×5=153 \times 5 = 15.
  • 15: This is the same as 3×102\frac{3 \times 10}{2} or 3×(10÷2)3 \times (10 \div 2).
  • 20: I know147=2\frac{14}{7} = 2 and 2×10=202 \times 10 = 20.
  • 20: This is equivalent to the last one.
Activity Synthesis (Teacher Notes)
  • “How can rearranging the numbers and operations help find the value of the last expression?” (I know that 147\frac{14}{7} is 2 so finding this first and then multiplying by 10 is easier than trying to work with the fraction 107\frac{10}{7}.)
Standards
Addressing
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

20 min